Torque

Mechanics · c. 250 BCE

Equation: τ = r × F, |τ| = r F sin θ
Field: Mechanics
Year: -250

Symbols

τ torque, a vector along the axis of rotation · r the lever arm from the axis to where the force acts · F the force · θ the angle between them

Significance

The turning effect of a force: bigger with a longer arm and a force at right angles to it, zero when you push along the arm. Archimedes had the law of the lever in 250 BCE; the vector form with the cross product is Gibbs's. It is what a motor delivers to its shaft, what a tap wrench applies to a thread, and what a wheel nut is torqued to.

Skills

Turning on a Lathe Tapping a Thread Follow, Draw and Stun

Machines

Brushed DC Motor Induction Motor Brushless Permanent-Magnet Motor Alternator Otto Four-Stroke Engine Diesel Engine Watt Steam Engine Steam Turbine

Requires

Cross Product

Required By

Tip Offset and Spin

Referenced by

equation

Cross Product Tip Offset and Spin

machine

Alternator Brushed DC Motor Brushless Permanent-Magnet Motor Diesel Engine Induction Motor Otto Four-Stroke Engine Steam Turbine Watt Steam Engine

skill

Follow, Draw and Stun Tapping a Thread Turning on a Lathe

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From the Equations database in Notion, last edited 2026-08-18. This page is the row, rendered by the build; nothing on it is written by hand.